Journal of Statistical Physics

, Volume 120, Issue 5–6, pp 1037–1100 | Cite as

Correction-to-Scaling Exponents for Two-Dimensional Self-Avoiding Walks

  • Sergio CaraccioloEmail author
  • Anthony J. Guttmann
  • Iwan Jensen
  • Andrea Pelissetto
  • Andrew N. Rogers
  • Alan D. Sokal

We study the correction-to-scaling exponents for the two-dimensional self-avoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up to 40 steps on the triangular lattice, measuring the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a monomer from the endpoints. The complete endpoint distribution is also calculated for self-avoiding walks up to 32 steps (square) and up to 22 steps (triangular). We also generate self-avoiding walks on the square lattice by Monte Carlo, using the pivot algorithm, obtaining the mean-square radii to ≈ 0.01% accuracy up to N=4000. We give compelling evidence that the first non-analytic correction term for two-dimensional self-avoiding walks is Δ1=3/2. We compute several moments of the endpoint distribution function, finding good agreement with the field-theoretic predictions. Finally, we study a particular invariant ratio that can be shown, by conformal-field-theory arguments, to vanish asymptotically, and we find the cancellation of the leading analytic correction.


Self-avoiding walk polymer exact enumeration series expansion Monte Carlo pivot algorithm corrections to scaling critical exponents conformal invariance 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Sergio Caracciolo
    • 1
    Email author
  • Anthony J. Guttmann
    • 2
  • Iwan Jensen
    • 2
  • Andrea Pelissetto
    • 3
  • Andrew N. Rogers
    • 2
  • Alan D. Sokal
    • 4
  1. 1.Dip. di Fisica and INFNUniversità di MilanoMilanoItaly
  2. 2.Department of Mathematics and StatisticsUniversity of MelbourneAustralia
  3. 3.Dip. di Fisica and INFN–Sezione di Roma IUniversità di Roma IRomaItaly
  4. 4.Department of PhysicsNew York UniversityNew YorkUSA

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